The mass of Pluto is $1.31 \times 10 ^ { 22 } \mathrm {~kg}$ and its radius is $1.15 \times 10 ^ { 6 } \mathrm {~m}$
What is the acceleration of a freely-falling object at the surface of Pluto if it has no atmosphere? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$
A) $0.661 \mathrm {~m} / \mathrm { s } ^ { 2 }$
B) $0.140 \mathrm {~m} / \mathrm { s } ^ { 2 }$
C) $9.81 \mathrm {~m} / \mathrm { s } ^ { 2 }$
D) $1.62 \mathrm {~m} / \mathrm { s } ^ { 2 }$
E) $3.72 \mathrm {~m} / \mathrm { s } ^ { 2 }$

Question

Quizplus · Accepted Answer

The acceleration due to gravity on the surface of a celestial body can be calculated using the formula $g = \frac{GM}{r^2}$, where $G$ is the gravitational constant, $M$ is the mass of the body, and $r$ is its radius. Substituting the given values for Pluto, $g = \frac{(6.67 \times 10^{-11} \mathrm{N} \cdot \mathrm{m}^2/\mathrm{kg}^2)(1.31 \times 10^{22} \mathrm{kg})}{(1.15 \times 10^6 \mathrm{m})^2}$ results in an acceleration of approximately $0.661 \mathrm{m/s}^2$.

The Mass of Pluto Is 1.31×1022 kg1.31 \times 10 ^ { 22 } \mathrm {~kg}1.31×1022 kg

The Mass of Pluto Is $1.31 \times 10 ^ { 22 } \mathrm {~kg}$